A plain text editor is a simple text programme such as Notepad. It will be any simple word processing software that produces files that when you save them end up with a .txt extension.
Simply launch Notepad, copy and paste your ebay Partner Network unique identifier into the file, then save the file.
You might be asked to name the file in a particular way, e.g. they might have asked you to name the filename the same as the unique identifier.
Once saved, you need to upload the .txt file to your server. Once it is on your server, epn will have a programme that automatically looks for it, recognises it and approves you.
The reason they do this is that it proves that you have control of your domain - the fact that you can place that file on your domain means you are the owner in their eyes - and their programme can open the file and read the unique identifier to confirm it.
I hope that helps.